document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164428>Question 164428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x)=-sqrt(1-x), determine f^-1(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121147 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-sqrt%281-x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-sqrt%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-sqrt%281-x%29 ALIGN=MIDDLE  ALT=\"y=-sqrt%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace f(x) with y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%281-y%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%281-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Switch x and y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x=sqrt%281-y%29 ALIGN=MIDDLE  ALT=\"-x=sqrt%281-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1-y ALIGN=MIDDLE  ALT=\"x%5E2=1-y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By=1 ALIGN=MIDDLE  ALT=\"x%5E2%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add y to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1-x%5E2 ALIGN=MIDDLE  ALT=\"y=1-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=-x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So the inverse function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29=-x%5E2%2B1 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29=-x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Note: the domain and range of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-sqrt%281-x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=-sqrt%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=1 ALIGN=MIDDLE  ALT=\"x%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=0 ALIGN=MIDDLE  ALT=\"y%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that the domain and range of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29=-x%5E2%2B1 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29=-x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=0 ALIGN=MIDDLE  ALT=\"x%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=1 ALIGN=MIDDLE  ALT=\"y%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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